An engel condition with skew derivations

Ming Chu Chou, Cheng Kai Liu

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Let R be a prime ring and set [x, y]1 = [x, y] = xy - yx for x, y ∈ R and inductively [x, y]k = [[x, y]k-1, y] for k > 1. We apply the theory of generalized polynomial identities with automorphisms and skew derivations to obtain the following result: If δ is a nonzero σ-derivation of R and L is a noncommutative Lie ideal of R so that [δ(x), x]k = 0 for all x ∈ L, where k is a fixed positive integer, then charR = 2 and for some field F. This result generalizes the case of derivations by Lanski and also the case of automorphisms by Mayne.

Original languageEnglish
Pages (from-to)259-270
Number of pages12
JournalMonatshefte fur Mathematik
Volume158
Issue number3
DOIs
Publication statusPublished - 2009 Jan 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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